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A006566
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Dodecahedral numbers: n(3n-1)(3n-2)/2.
(Formerly M5089)
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17
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0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, 14190, 17296, 20825, 24804, 29260, 34220, 39711, 45760, 52394, 59640, 67525, 76076, 85320, 95284, 105995, 117480, 129766, 142880, 156849, 171700, 187460, 204156
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Schlaefli symbol for this polyhedron: {5,3}
A093485 = first differences; A124388 = second differences; third differences = 27. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 30 2006
One of the 5 Platonic polyhedral (tetrahedral, cube, octahedral, dodecahedral and icosahedral) numbers (cf. A053012). [From Daniel Forgues (squid(AT)zensearch.com), May 14 2010]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Tanya Khovanova, Recursive Sequences
Hyun Kwang Kim, On Regular Polytope Numbers
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: x(1+16x+10x^2)/(1-x)^4. a(n) = A000292(3n-3) = A054776(n)/6 = n*A060544(n).
a(n) = C(n+2,3) + 16 C(n+1,3) + 10 C(n,3)
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MAPLE
| A006566:=(1+16*z+10*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[n(3n-1)(3n-2)/2, {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
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PROG
| (PARI) a(n)=n*(3*n-1)*(3*n-2)/2
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CROSSREFS
| Sequence in context: A044207 A044588 A172221 * A205312 A154077 A027849
Adjacent sequences: A006563 A006564 A006565 * A006567 A006568 A006569
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Nov 23 2001
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